October 18, 2022

Exponential EquationsExplanation, Solving, and Examples

In math, an exponential equation takes place when the variable shows up in the exponential function. This can be a frightening topic for kids, but with a some of instruction and practice, exponential equations can be determited simply.

This blog post will discuss the explanation of exponential equations, kinds of exponential equations, proceduce to work out exponential equations, and examples with answers. Let's began!

What Is an Exponential Equation?

The first step to work on an exponential equation is determining when you have one.

Definition

Exponential equations are equations that have the variable in an exponent. For instance, 2x+1=0 is not an exponential equation, but 2x+1=0 is an exponential equation.

There are two key things to keep in mind for when you seek to determine if an equation is exponential:

1. The variable is in an exponent (meaning it is raised to a power)

2. There is only one term that has the variable in it (aside from the exponent)

For example, check out this equation:

y = 3x2 + 7

The primary thing you must note is that the variable, x, is in an exponent. Thereafter thing you should observe is that there is another term, 3x2, that has the variable in it – not only in an exponent. This implies that this equation is NOT exponential.

On the flipside, take a look at this equation:

y = 2x + 5

Yet again, the first thing you must note is that the variable, x, is an exponent. The second thing you must observe is that there are no other terms that includes any variable in them. This means that this equation IS exponential.


You will run into exponential equations when you try solving diverse calculations in algebra, compound interest, exponential growth or decay, and various distinct functions.

Exponential equations are essential in math and perform a central role in figuring out many math questions. Therefore, it is important to completely understand what exponential equations are and how they can be used as you move ahead in arithmetic.

Varieties of Exponential Equations

Variables occur in the exponent of an exponential equation. Exponential equations are remarkable ordinary in everyday life. There are three main kinds of exponential equations that we can figure out:

1) Equations with identical bases on both sides. This is the easiest to work out, as we can simply set the two equations equal to each other and work out for the unknown variable.

2) Equations with distinct bases on each sides, but they can be created similar employing rules of the exponents. We will put a few examples below, but by converting the bases the equal, you can follow the exact steps as the first case.

3) Equations with distinct bases on both sides that cannot be made the same. These are the most difficult to figure out, but it’s attainable through the property of the product rule. By increasing both factors to similar power, we can multiply the factors on both side and raise them.

Once we have done this, we can determine the two new equations identical to each other and figure out the unknown variable. This blog does not include logarithm solutions, but we will let you know where to get help at the end of this blog.

How to Solve Exponential Equations

From the explanation and kinds of exponential equations, we can now understand how to work on any equation by following these simple procedures.

Steps for Solving Exponential Equations

There are three steps that we are required to follow to work on exponential equations.

Primarily, we must determine the base and exponent variables in the equation.

Next, we need to rewrite an exponential equation, so all terms are in common base. Thereafter, we can work on them using standard algebraic techniques.

Third, we have to work on the unknown variable. Once we have solved for the variable, we can plug this value back into our first equation to discover the value of the other.

Examples of How to Work on Exponential Equations

Let's check out some examples to observe how these steps work in practice.

Let’s start, we will work on the following example:

7y + 1 = 73y

We can notice that both bases are the same. Hence, all you need to do is to restate the exponents and figure them out through algebra:

y+1=3y

y=½

Now, we change the value of y in the specified equation to corroborate that the form is real:

71/2 + 1 = 73(½)

73/2=73/2

Let's observe this up with a more complicated sum. Let's work on this expression:

256=4x−5

As you can see, the sides of the equation do not share a similar base. Despite that, both sides are powers of two. As such, the working includes breaking down respectively the 4 and the 256, and we can alter the terms as follows:

28=22(x-5)

Now we work on this expression to find the ultimate result:

28=22x-10

Carry out algebra to work out the x in the exponents as we performed in the last example.

8=2x-10

x=9

We can double-check our workings by substituting 9 for x in the initial equation.

256=49−5=44

Keep searching for examples and questions online, and if you use the properties of exponents, you will turn into a master of these theorems, solving most exponential equations with no issue at all.

Improve Your Algebra Abilities with Grade Potential

Working on problems with exponential equations can be difficult without help. Even though this guide covers the fundamentals, you still may face questions or word problems that might stumble you. Or perhaps you need some further guidance as logarithms come into the scene.

If you feel the same, contemplate signing up for a tutoring session with Grade Potential. One of our expert tutors can help you better your skills and confidence, so you can give your next examination a grade-A effort!